Great topic, let's compare and contrast the two artists to answer the question - I have had theories on this from the 60's.
In addition to the excellent points made in the other posts, consider:
THE WRTERS:
Even in the Beatles late days, the principal writer would present and perform his composition to the "committee" - the other Beatles. They, then helped refine, finish or add bits to the song, via the playing-pre-recording and recording process. So even the most singular Beatle song had the group imput. THEY interpreted the song BEFORE it was fully born. So, an artist, is actually attempting to interpret the imput of four musicians, not one - when they attempt a Beatle song. The best results have been by artists who have not attempted to interpret a Beatle song, but already have their own distinct style and simply sing the same lyrics, but the music is not. Example: Joe Cocker's WALHFMF and Richie Haven's HCTS - those cats could recite "Happy Birthday" and it'll have their stamp on it. Not so, most other artists.
All of the above is even more true, for their early-mid compositions, which were even more collaberative.
Dylan was interpreting Woody Guthrie, Pete Seeger, Phil Ochs and other folk illuminaries with his own lyrics, songs, but the style, spirit and intent already existed and he was building and expanding on that. In fact, Dylan often changes his own songs, live in concert, creating different versions of the same song. He does not "finish" a song and preserve it. Beatles were not interpreting, they were creating- having ASSIMULATED many of their inspirational artists - to then create a new sound and mixture of music, the whole being greater than the assembled influences, added-up seperately. The Beatles - and John, George , Paul and Ringo Concerts preserved "the song" with little or no improvisation.
THE VOICES: You can't top the Beatles, individual, harmony, counter-harmony, duet, multi-tracked voices - whatever. Again, the best and really only way to "interpret" their songs, is to sing them in your own voice and style, as noted above and, say Emmylou Harris' cover of HT+E. Dylan offers vast opportunities for covers, as noted in other posts and specifically, in this chapter his voice. He is almost reading his own poetry, so a musical voice is offering something new to the song in a "cover" version. (Too many examples to list here.) Let's use Mr. Tambourine Man as an example with Dylan, you add the Byrds' voices, harmonies, interpretive phrasings, multi-instrumentations, 12- string Rickenbacker, 6--string, tambourine, bass and drums. IF the Beatles had written this, they would have ALREADY provided all of the above elements the Byrds ultimately added. They were a group, Dylan was not. They were singers, he was not, he did "sing" in a poetry - later "rock' voice, but not in a musical way.
THE LYRICS: Dylan's are brilliant, complex and evoke many interpretations. The Beatles had elements of
all those in their lyrics, but their lyrics were more specific, finite and part of the music, they wrote in musical language, primarily, not in word-thought sketches. Once again, more elements to play with for an artist in the Dylan song, than the Beatles one. The beginning of a Beatles' song sketch or demo, left the others to chip in with the lyrics, linguistically shape the words to the music and add or subtract a lyric here or there - The Beatles interpreted the songs of John Lennon, Paul McCartney and George Harrison. The band process was different. When Dylan, occassionally wrote with others in a "band" -style experience, the songs were better defined. Example: Writing some lyrics for the Byrds "Easy Rider", "If Not For You" with George Harrison, those songs are better defined.
What greatness!
